Question

`sqrt2x^2+7+5sqrt2=0`

Answer 1

The given equation is `sqrt2x^2+7+5sqrt2=0` 

Comparing it with` ax^2+bx+c=0,`  we get 

`a=sqrt2, b=7 and c=5sqrt2` 

∴ Discriminant, `D=b^2-4ac=(7)^2-4xxsqrt2xx5sqrt2=49-40=9>0` 

So, the given equation has real roots.
Now, `sqrt(D)=sqrt(9)=3` 

∴ `α=(-b+sqrt(D))/(2a)=(-7+3)/(2xxsqrt(2))=-4/(2sqrt2)=-sqrt2` 

β=`(-b-sqrt(D))/(2a)=(-7-3)/(2xxsqrt(2))=-4/(2sqrt2)=-sqrt2` 

Hence, `-sqrt(2)`and `-(5sqrt2)/2`are the root of the given equation.